What you have written is correct but I can explain it more. First, it is important to understand that a probability is found by dividing the part by the whole (in this case, the whole is always going to be 50 total flips). For the probability of the cup landing open side up, you would do 2/50 which is the same as 0.04. For the probability of the cup landing closed side up, you would do 6/50 which is the same as 0.12. For the probability of the cup landing on its side, you would do 42/50 which is the same as 0.84.
One way to check your work is to find the sum of the probabilities of all possible outcomes, and the sum should equal 1. In this case, you know you are correct because 0.04+0.12+0.84=1.